55:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000
Pensamiento numérico y variacional :@0.603816:0.043660:0.930949:0.043660:0.930949:0.024915:0.603816:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 1:@0.073089:0.136836:0.149461:0.136836:0.149461:0.120167:0.073089:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un fabricante de:@0.073089:0.160620:0.195138:0.160620:0.195138:0.144186:0.073089:0.144186:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 jeans:@0.195000:0.160620:0.234907:0.160620:0.234907:0.144214:0.195000:0.144214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 obtiene una ganancia de $30 por cada :@0.234889:0.160620:0.526220:0.160620:0.526220:0.144186:0.234889:0.144186:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
jean:@0.526367:0.160620:0.556371:0.160620:0.556371:0.144214:0.526367:0.144214:0.000000:0.000000:0.000000:0.000000
 de marca :@0.556334:0.160620:0.632905:0.160620:0.632905:0.144186:0.556334:0.144186:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Blue:@0.633203:0.160620:0.662765:0.160620:0.662765:0.144214:0.633203:0.144214:0.000000:0.000000:0.000000:0.000000
 y $15 :@0.662728:0.160620:0.710403:0.160620:0.710403:0.144186:0.662728:0.144186:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por cada :@0.073089:0.177262:0.146092:0.177262:0.146092:0.160828:0.073089:0.160828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
jean:@0.148411:0.177262:0.179354:0.177262:0.179354:0.160856:0.148411:0.160856:0.000000:0.000000:0.000000:0.000000
 de marca :@0.179648:0.177262:0.262868:0.177262:0.262868:0.160828:0.179648:0.160828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Victoria:@0.265187:0.177262:0.320418:0.177262:0.320418:0.160856:0.265187:0.160856:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Para la fabricación de sus pantalones utiliza dos :@0.320722:0.177262:0.710462:0.177262:0.710462:0.160828:0.320722:0.160828:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
máquinas:   y  . Para la fabricación del pantalón de marca Blue, la máquina   demora 15 :@0.073070:0.193904:0.710387:0.193904:0.710387:0.177470:0.073070:0.177470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B:@0.151320:0.193904:0.185299:0.193904:0.185299:0.177498:0.151320:0.177498:0.000000:0.000000:0.000000
A:@0.614170:0.193904:0.624055:0.193904:0.624055:0.177498:0.614170:0.177498:0.000000
minutos y la máquina  , 9 minutos. Para la elaboración del pantalón de marca :@0.073034:0.210546:0.634849:0.210546:0.634849:0.194112:0.073034:0.194112:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.233048:0.210546:0.241883:0.210546:0.241883:0.194140:0.233048:0.194140:0.000000
Victoria:@0.634344:0.210546:0.687254:0.210546:0.687254:0.194140:0.634344:0.194140:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, la :@0.687228:0.210546:0.710311:0.210546:0.710311:0.194112:0.687228:0.194112:0.000000:0.000000:0.000000:0.000000:0.000000
máquina   demora 5 minutos y la máquina  , 3 minutos. Si diariamente cuenta con la :@0.073015:0.227188:0.710418:0.227188:0.710418:0.210754:0.073015:0.210754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.142871:0.227188:0.152755:0.227188:0.152755:0.210781:0.142871:0.210781:0.000000
B:@0.397701:0.227188:0.406536:0.227188:0.406536:0.210781:0.397701:0.210781:0.000000
máquina   un máximo de 200 minutos y con la  , un máximo de 90 minutos, ¿cuántos :@0.073034:0.243829:0.710125:0.243829:0.710125:0.227396:0.073034:0.227396:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.142171:0.243829:0.152056:0.243829:0.152056:0.227423:0.142171:0.227423:0.000000
B:@0.424134:0.243829:0.432969:0.243829:0.432969:0.227423:0.424134:0.227423:0.000000
pantalones de cada tipo debe producir para obtener la máxima utilidad?:@0.073015:0.260471:0.598180:0.260471:0.598180:0.244037:0.073015:0.244037:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Identificamos las variables y organizamos en una tabla.:@0.073015:0.284255:0.469069:0.284255:0.469069:0.267821:0.073015:0.267821:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Solución:@0.073015:0.315195:0.139668:0.315195:0.139668:0.298526:0.073015:0.298526:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.193501:0.344620:0.197312:0.344620:0.197312:0.327673:0.193501:0.327673:0.000000
Máquina A :@0.323077:0.344620:0.412221:0.344620:0.412221:0.327673:0.323077:0.327673:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Máquina B:@0.451701:0.344620:0.535931:0.344620:0.535931:0.327673:0.451701:0.327673:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ganancia:@0.584900:0.344620:0.658875:0.344620:0.658875:0.327673:0.584900:0.327673:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Pantalones marca :@0.100043:0.365274:0.221464:0.365274:0.221464:0.350120:0.100043:0.350120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Blue (x):@0.221129:0.365274:0.268118:0.365274:0.268118:0.350108:0.221129:0.350108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.248690:0.365274:0.252237:0.365274:0.252237:0.350120:0.248690:0.350120:0.000000
15:@0.356790:0.366062:0.374682:0.366062:0.374682:0.349629:0.356790:0.349629:0.000000:0.000000
9:@0.489323:0.366062:0.498305:0.366062:0.498305:0.349629:0.489323:0.349629:0.000000
$30:@0.608491:0.366062:0.635292:0.366062:0.635292:0.349629:0.608491:0.349629:0.000000:0.000000:0.000000
Pantalones marca :@0.100043:0.386717:0.221464:0.386717:0.221464:0.371563:0.100043:0.371563:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Victoria (y):@0.221129:0.386717:0.289571:0.386717:0.289571:0.371550:0.221129:0.371550:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.270143:0.386717:0.273690:0.386717:0.273690:0.371563:0.270143:0.371563:0.000000
5:@0.361242:0.387505:0.370224:0.387505:0.370224:0.371071:0.361242:0.371071:0.000000
3:@0.489319:0.387505:0.498302:0.387505:0.498302:0.371071:0.489319:0.371071:0.000000
$15:@0.608488:0.387505:0.635289:0.387505:0.635289:0.371071:0.608488:0.371071:0.000000:0.000000:0.000000
Tiempo disponible :@0.100043:0.408160:0.228274:0.408160:0.228274:0.393006:0.100043:0.393006:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(min):@0.227940:0.408160:0.262395:0.408160:0.262395:0.392993:0.227940:0.392993:0.000000:0.000000:0.000000:0.000000:0.000000
200:@0.352339:0.408948:0.379140:0.408948:0.379140:0.392514:0.352339:0.392514:0.000000:0.000000:0.000000
90:@0.484871:0.408948:0.502763:0.408948:0.502763:0.392514:0.484871:0.392514:0.000000:0.000000
Como la producción de un artículo no puede ser negativa, tenemos:   ≥ 0,   ≥ 0.  :@0.073101:0.446156:0.710397:0.446156:0.710397:0.429722:0.073101:0.429722:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.613336:0.446156:0.620809:0.446156:0.620809:0.429750:0.613336:0.429750:0.000000
x:@0.662998:0.446156:0.670453:0.446156:0.670453:0.429750:0.662998:0.429750:0.000000
Al referirse el problema a lza máxima ganancia, significa menor o igual ≤. Entonces, :@0.073119:0.462798:0.676642:0.462798:0.676642:0.446364:0.073119:0.446364:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
15  + 5  ≤ 200; 9  + 3  ≤ 90:@0.073119:0.483018:0.274035:0.483018:0.274035:0.466584:0.073119:0.466584:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.090919:0.483018:0.098374:0.483018:0.098374:0.466612:0.090919:0.466612:0.000000
y:@0.125985:0.483018:0.133458:0.483018:0.133458:0.466612:0.125985:0.466612:0.000000
x:@0.194865:0.483018:0.202320:0.483018:0.202320:0.466612:0.194865:0.466612:0.000000
y:@0.229931:0.483018:0.237404:0.483018:0.237404:0.466612:0.229931:0.466612:0.000000
Por lo tanto, el sistema de inecuaciones es:  :@0.073083:0.533415:0.388629:0.533415:0.388629:0.516981:0.073083:0.516981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.409964:0.501385:0.418070:0.501385:0.422997:0.484514:0.414890:0.484514:0.000000
y:@0.444544:0.501385:0.452858:0.501385:0.457784:0.484514:0.449470:0.484514:0.000000
x:@0.402927:0.522724:0.411034:0.522724:0.415960:0.505854:0.407853:0.505854:0.000000
y:@0.437507:0.522724:0.445822:0.522724:0.450748:0.505854:0.442433:0.505854:0.000000
y:@0.394292:0.544079:0.402606:0.544079:0.407532:0.527208:0.399218:0.527208:0.000000
x:@0.393538:0.565454:0.401644:0.565454:0.406571:0.548584:0.398464:0.548584:0.000000
15:@0.393006:0.501374:0.411241:0.501374:0.411241:0.484504:0.393006:0.484504:0.000000:0.000000
5:@0.435843:0.501374:0.445065:0.501374:0.445065:0.484504:0.435843:0.484504:0.000000
200:@0.472729:0.501374:0.499977:0.501374:0.499977:0.484504:0.472729:0.484504:0.000000:0.000000:0.000000
9:@0.394187:0.522719:0.403409:0.522719:0.403409:0.505848:0.394187:0.505848:0.000000
3:@0.428805:0.522719:0.438026:0.522719:0.438026:0.505848:0.428805:0.505848:0.000000
90:@0.465690:0.522719:0.483925:0.522719:0.483925:0.505848:0.465690:0.505848:0.000000:0.000000
0:@0.422475:0.544088:0.431696:0.544088:0.431696:0.527218:0.422475:0.527218:0.000000
0:@0.420920:0.565439:0.430141:0.565439:0.430141:0.548569:0.420920:0.548569:0.000000
:@0.407768:0.544683:0.423509:0.544683:0.423509:0.526559:0.407768:0.526559:0.000000
:@0.406212:0.566037:0.421953:0.566037:0.421953:0.547914:0.406212:0.547914:0.000000
Graficando las rectas, obtenemos: (Figura 1). :@0.073089:0.599277:0.394362:0.599277:0.394362:0.582844:0.073089:0.582844:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.316488:0.599277:0.319801:0.599277:0.319801:0.582871:0.316488:0.582871:0.000000
Sombreamos la solución de cada inecuación; recuerda que la solución del sistema es la :@0.073070:0.626639:0.709932:0.626639:0.709932:0.610206:0.073070:0.610206:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
intersección de las regiones sombreadas (región factible). (Figura 2).:@0.073070:0.643281:0.551284:0.643281:0.551284:0.626847:0.073070:0.626847:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Verificamos la solución tomando un punto de la intersección de las regiones sombreadas. :@0.073070:0.670643:0.710099:0.670643:0.710099:0.654209:0.073070:0.654209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
P (0, 10).:@0.073070:0.687285:0.132820:0.687285:0.132820:0.670851:0.073070:0.670851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
15(0)5(10) 200 50 200:@0.073089:0.712390:0.276756:0.712390:0.276756:0.695956:0.073089:0.695956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
9(0) 3(10)90:@0.074239:0.733182:0.185879:0.733182:0.185879:0.716749:0.074239:0.716749:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
10 0:@0.073089:0.753985:0.115383:0.753985:0.115383:0.737551:0.073089:0.737551:0.000000:0.000000:0.000000:0.000000
;:@0.203204:0.743431:0.206406:0.743431:0.206406:0.726997:0.203204:0.726997:0.000000
30 90:@0.216895:0.733182:0.267975:0.733182:0.267975:0.716749:0.216895:0.716749:0.000000:0.000000:0.000000:0.000000:0.000000
10 0:@0.215754:0.753985:0.258054:0.753985:0.258054:0.737551:0.215754:0.737551:0.000000:0.000000:0.000000:0.000000
La solución satisface el sistema de inecuaciones.:@0.073089:0.790161:0.414335:0.790161:0.414335:0.773727:0.073089:0.773727:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La función que representa la ganancia máxima :@0.073089:0.817523:0.418578:0.817523:0.418578:0.801089:0.073089:0.801089:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es  ( ,  ) = 30  + 15 . Para determinar la ganancia :@0.073089:0.834164:0.418738:0.834164:0.418738:0.817731:0.073089:0.817731:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x y:@0.091956:0.834164:0.122236:0.834164:0.122236:0.817758:0.091956:0.817758:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.161959:0.834164:0.169414:0.834164:0.169414:0.817758:0.161959:0.817758:0.000000
y:@0.204517:0.834164:0.211990:0.834164:0.211990:0.817758:0.204517:0.817758:0.000000
máxima, reemplazo los vértices en esta función.:@0.073052:0.850806:0.409951:0.850806:0.409951:0.834372:0.073052:0.834372:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La ganancia máxima es $450 y se produce :@0.073052:0.878168:0.418575:0.878168:0.418575:0.861734:0.073052:0.861734:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuando se fabrican 30 pantalones marca :@0.073052:0.894810:0.360684:0.894810:0.360684:0.878376:0.073052:0.878376:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Victoria:@0.360040:0.894810:0.411652:0.894810:0.411652:0.878404:0.360040:0.878404:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
.:@0.411377:0.894810:0.414580:0.894810:0.414580:0.878376:0.411377:0.878376:0.000000
y:@0.814410:0.631856:0.820484:0.631856:0.820484:0.619531:0.814410:0.619531:0.000000
x:@0.916247:0.701498:0.922170:0.701498:0.922170:0.689174:0.916247:0.689174:0.000000
0:@0.818494:0.706882:0.823734:0.706882:0.823734:0.697296:0.818494:0.697296:0.000000
60:@0.811080:0.650563:0.821559:0.650563:0.821559:0.640978:0.811080:0.640978:0.000000:0.000000
40:@0.811080:0.666943:0.821559:0.666943:0.821559:0.657357:0.811080:0.657357:0.000000:0.000000
20:@0.811080:0.683321:0.821559:0.683321:0.821559:0.673736:0.811080:0.673736:0.000000:0.000000
–20:@0.805711:0.716083:0.821559:0.716083:0.821559:0.706497:0.805711:0.706497:0.000000:0.000000:0.000000
–40:@0.805711:0.732464:0.821559:0.732464:0.821559:0.722878:0.805711:0.722878:0.000000:0.000000:0.000000
20:@0.843446:0.706882:0.853926:0.706882:0.853926:0.697296:0.843446:0.697296:0.000000:0.000000
–20:@0.796408:0.706882:0.812255:0.706882:0.812255:0.697296:0.796408:0.697296:0.000000:0.000000:0.000000
–40:@0.774665:0.706882:0.790513:0.706882:0.790513:0.697296:0.774665:0.697296:0.000000:0.000000:0.000000
–60:@0.752923:0.706882:0.768771:0.706882:0.768771:0.697296:0.752923:0.697296:0.000000:0.000000:0.000000
40:@0.865178:0.706882:0.875657:0.706882:0.875657:0.697296:0.865178:0.697296:0.000000:0.000000
60:@0.886920:0.706882:0.897399:0.706882:0.897399:0.697296:0.886920:0.697296:0.000000:0.000000
3x + y = 40:@0.740088:0.646074:0.795467:0.646074:0.795467:0.634962:0.740088:0.634962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3x + y = 30:@0.745118:0.658211:0.800497:0.658211:0.800497:0.647099:0.745118:0.647099:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 1:@0.885057:0.759001:0.925727:0.759001:0.925727:0.747070:0.885057:0.747070:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Figura 2:@0.883865:0.937150:0.924535:0.937150:0.924535:0.925218:0.883865:0.925218:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.815010:0.777694:0.821085:0.777694:0.821085:0.765369:0.815010:0.765369:0.000000
x:@0.917525:0.887035:0.923447:0.887035:0.923447:0.874711:0.917525:0.874711:0.000000
0:@0.802942:0.885464:0.808182:0.885464:0.808182:0.875878:0.802942:0.875878:0.000000
30:@0.792701:0.789001:0.803180:0.789001:0.803180:0.779415:0.792701:0.779415:0.000000:0.000000
25:@0.792701:0.803990:0.803180:0.803990:0.803180:0.794405:0.792701:0.794405:0.000000:0.000000
20:@0.792701:0.818980:0.803180:0.818980:0.803180:0.809394:0.792701:0.809394:0.000000:0.000000
15:@0.792701:0.833980:0.803180:0.833980:0.803180:0.824395:0.792701:0.824395:0.000000:0.000000
10:@0.792701:0.849261:0.803180:0.849261:0.803180:0.839675:0.792701:0.839675:0.000000:0.000000
5:@0.797941:0.864542:0.803180:0.864542:0.803180:0.854956:0.797941:0.854956:0.000000
–5:@0.793867:0.894660:0.804475:0.894660:0.804475:0.885075:0.793867:0.885075:0.000000:0.000000
–10:@0.788627:0.909901:0.804475:0.909901:0.804475:0.900315:0.788627:0.900315:0.000000:0.000000:0.000000
5:@0.827616:0.885464:0.832856:0.885464:0.832856:0.875878:0.827616:0.875878:0.000000
10 15 20:@0.846008:0.885464:0.896386:0.885464:0.896386:0.875878:0.846008:0.875878:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–5:@0.785227:0.885464:0.795835:0.885464:0.795835:0.875878:0.785227:0.875878:0.000000:0.000000
–10:@0.762550:0.885464:0.778398:0.885464:0.778398:0.875878:0.762550:0.875878:0.000000:0.000000:0.000000
La región factible puede :@0.740294:0.347321:0.905907:0.347321:0.905907:0.332382:0.740294:0.332382:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ser::@0.740294:0.362450:0.762801:0.362450:0.762801:0.347510:0.740294:0.347510:0.000000:0.000000:0.000000:0.000000
Acotada:@0.740294:0.384728:0.795750:0.384728:0.795750:0.369788:0.740294:0.369788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.740294:0.473837:0.743958:0.473837:0.743958:0.458897:0.740294:0.458897:0.000000
No acotada:@0.740294:0.496115:0.816968:0.496115:0.816968:0.481175:0.740294:0.481175:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.740294:0.305721:0.848854:0.305721:0.848854:0.288774:0.740294:0.288774:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.740294:0.322362:0.837769:0.322362:0.837769:0.305415:0.740294:0.305415:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Y:@0.766399:0.400154:0.773401:0.400154:0.773401:0.387726:0.766399:0.387726:0.000000
X:@0.888371:0.460690:0.895971:0.460690:0.895971:0.448262:0.888371:0.448262:0.000000
Y:@0.767287:0.512059:0.774021:0.512059:0.774021:0.500107:0.767287:0.500107:0.000000
X:@0.888199:0.581451:0.895509:0.581451:0.895509:0.569499:0.888199:0.569499:0.000000
Vértice:@0.461948:0.808704:0.517107:0.808704:0.517107:0.791757:0.461948:0.791757:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f(x, y) = :@0.556817:0.808704:0.615739:0.808704:0.615739:0.791757:0.556817:0.791757:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
30:@0.615728:0.808704:0.635387:0.808704:0.635387:0.791757:0.615728:0.791757:0.000000:0.000000
x + :@0.635314:0.808704:0.661489:0.808704:0.661489:0.791757:0.635314:0.791757:0.000000:0.000000:0.000000:0.000000
15:@0.661434:0.808704:0.681093:0.808704:0.681093:0.791757:0.661434:0.791757:0.000000:0.000000
y:@0.681019:0.808704:0.689707:0.808704:0.689707:0.791757:0.681019:0.791757:0.000000
(0, 30):@0.467550:0.835192:0.511488:0.835192:0.511488:0.818758:0.467550:0.818758:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
30(0) + 15(30) = 450 :@0.549554:0.835192:0.700991:0.835192:0.700991:0.818758:0.549554:0.818758:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(0, 0):@0.472041:0.859891:0.506997:0.859891:0.506997:0.843457:0.472041:0.843457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
30(0) + 15(0) = 0:@0.563029:0.859891:0.683486:0.859891:0.683486:0.843457:0.563029:0.843457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(10, 0):@0.467550:0.884590:0.511488:0.884590:0.511488:0.868157:0.467550:0.868157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
30(10) + 15(0) = 30:@0.554046:0.884590:0.692468:0.884590:0.692468:0.868157:0.554046:0.868157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(Ev.) Grafica las áreas de solución de sistemas de inecuaciones:@0.081717:0.971366:0.406053:0.971366:0.406053:0.959414:0.081717:0.959414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000